Long post incoming. Yes, I'm a total sucker for ninja games.
Games I've personally beaten and consider to be amazing:
Strider (Arcade, PS1. Genesis version is just not as good. This is one of my all-time favorite games.)
Strider 2 (Arcade, PS1. Even better than the first, if you can believe that.)
Strider (PC, Xbox One, PS4. Against all odds, an incredible sequel to the originals mixing elements of Strider arcade, Strider NES and Strider 2 arcade. Brilliant game and one of my favorites this generation)
Shinobi (Arcade Ver. The OG, and still just as good as the first day)
Shinobi 3 (MegaDrive. One of the best games of the SNES/MD generation. You'd be hard pressed to find a better action game.)
Ninja Gaiden (NES. The OG Ninja Gaiden and one of the finest examples of 2D action)
Ninja Gaiden Black / Sigma (Xbox, PS3, I personally prefer Sigma but Black seems to have more supporters)
Ninja Gaiden 2 / Sigma (Xbox 360, PS3, again I personally prefer Sigma but people seem to like vanilla NG2 better)
Ninja Gaiden 3: Razor's Edge (Wii U version has heavy frame drops, 360 has the best framerate but has more screen tearing, I find the PS3 version to be nicely balanced)
Tenchu: Wrath of Heaven (PS2, Xbox. Stealth-based. Never played it on Xbox though)
Shinobido (PS2, Stealth-based, probably the best stealth ninja game to date)
Metal Gear Rising: Revengeance (PC, Xbox 360, PS3. This game is fucking nuts. I love it, and you should too. One of the finest 3D action games ever made)
Ragnarok Online (PC. Combination of stealth and action. Play the Ninja / Kagerou/ Oboro class, my favorite MMO ninja class by far)
Games I've played briefly and enjoyed but haven't gotten to play extensively yet:
Ni-Oh (PS4, by far the best game in this subcategory. Played the last beta extensively and loved it but I don't have the full game yet)
Shinobi (PS2)
Final Fantasy 14 ARR (PC, Ninja class. Feels a bit less ninja-like to me, but I need to play more)
Ninja Gaiden (Master System. Pretty good, didn't grab me as much as Ninja Gaiden NES but I liked what I played better than either of the NES sequels)
The Ninjawarriors (SNES. I really love the gameplay and especially the kunoichi character, but I haven't played it too much. Really need to, though.)
Hagane (SNES. Mix of Shinobi's ranged focus and Ninja Gaiden's melee focus. I really liked it, but I need to dive deeper into it)
Games I've played, didn't really like but are generally acclaimed:
Revenge of Shinobi (MegaDrive)
Ninja Gaiden 2 (NES)
Ninja Gaiden 3 (NES)
Tenchu (PS1. Liked it back in the day but holy shit has it aged poorly. The controls are just shit)
Tenchu 2: Birth of the Stealth Assassins (PS1. See above)
Mark of the Ninja (PC, Xbox 360. Feels too much like a puzzle minigame collection than either an action or stealth game. Instead of using the game's core mechanics to sneak around, there's too much emphasis on finding the correct solution or item for each specific set-piece)
Games I've never played but might be good:
Nightshade (PS2)
Shinobido 2 (PS Vita)
Games I've played and didn't like:
Ninja Blade (PC, 360)
Ninja Five-O (GBA)
Tenchu: Shadow Assassins (Wii, PSP. Way too linear. Mechanics just feel weird and you're pretty much railroaded the whole way through)
Shinobido (PSP version, feels too haphazardly designed. Almost like a collection of bonus, minigame-like levels)
Shadow of the Ninja (NES, enemy placement, attack patterns and overall physics are just weird IMO)
Games I liked but others generally don't:
Strider (NES, quite possibly the jankiest game I've ever loved. Collision detection is a mess but damn if I don't love it for some reason.)
Tenchu Z (Xbox 360. Stealth-based. Fair warning: It feels more like a PS2-gen game
than a 360/PS3-gen game)
Tenchu: Time of the Assassins (PSP. View distance is atrocious but I found it to have really good graphics and gameplay mechanics. Memorization, careful progression and the Ki detector mitigate the view distance issue.